Write the point-slope form of an equation of the line through the points (-1, 4) and (-2, 2).

Answers

Answer 1

Answer:

Point-slope form: y-4=2(x+1)

Slope intercept form: y=2x+6

I hope this helps!

Answer 2

Answer:

[tex]y-4=2(x+1)[/tex]

Step-by-step explanation:

Point-slope form is equal to

[tex]y-y_1=m(x-x_1)[/tex]

where y and y1 are the known y coordinates of two points on the line, and x and x1 are the known x coordinates of two points on the line. All we need now is m, which is the slope:

[tex]4-2=m(-1-(-2))[/tex]

We can simplify negative one minus negative two as positive 1.

[tex]4-2=m(1)[/tex]

4 minus 2 is 2, so m times 1 is 2. That means m is 2.

Now, we have the slope, so we can convert to point-slope form using one of the two points. Let's use (-1, 4). We can plug those values in for x1 and y1:

[tex]y-4=2(x+1)[/tex]


Related Questions

Identify the terminal point for a 45° angle in a unit circle.
O A (231)
O B.
O c.
V2 72

Answers

Answer:

D

Step-by-step explanation:

x- coordinate = cos45° = [tex]\frac{1}{\sqrt{2} }[/tex] = [tex]\frac{\sqrt{2} }{2}[/tex]

y- coordinate = sin45° = [tex]\frac{1}{\sqrt{2} }[/tex] = [tex]\frac{\sqrt{2} }{2}[/tex]

That is ( [tex]\frac{\sqrt{2} }{2}[/tex] , [tex]\frac{\sqrt{2} }{2}[/tex] ) → D

If x+y=8 and xy =15 find the value of x³+y³.​

Answers

Answer:

152

Step-by-step explanation:

let x= 5 and y= 3x + y = 85 + 3 = 8xy = 155 × 3 = 15x³ + y³ = ?5³ + 3³ = ?125 + 27 = 152

[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]

A quality control expert at Glotech computers wants to test their new monitors. The production manager claims they have a mean life of 83 months with a variance of 81. If the claim is true, what is the probability that the mean monitor life would be greater than 81.2 months in a sample of 146 monitors? Round your answer to four decimal places.

Answers

Answer:

0.9922 = 99.22% probability that the mean monitor life would be greater than 81.2 months in a sample of 146 monitors.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

The production manager claims they have a mean life of 83 months with a variance of 81.

This means that [tex]\mu = 83, \sigma = \sqrt{81} = 9[/tex]

Sample of 146:

This means that [tex]n = 146, s = \frac{9}{\sqrt{146}}[/tex]

What is the probability that the mean monitor life would be greater than 81.2 months in a sample of 146 monitors?

This is 1 subtracted by the p-value of Z when X = 81.2. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{81.2 - 83}{\frac{9}{\sqrt{146}}}[/tex]

[tex]Z = -2.42[/tex]

[tex]Z = -2.42[/tex] has a p-value of 0.0078.

1 - 0.0078 = 0.9922.

0.9922 = 99.22% probability that the mean monitor life would be greater than 81.2 months in a sample of 146 monitors.

If a teacher's guide to a popular SAT workbook is to be printed using a special type of paper, the guide must have at most 400 pages. If the publishing company charges 1 cent per page printed, what is the largest price, in dollars, that can be charged to print 20 copies of the workbook using the special paper?

Answers

Answer:

$80

Step-by-step explanation:

To find the largest price, assume that all 20 copies of the workbook will have 400 pages.

Since the company charges 1 cent per page, this means each workbook will cost 400 cents. This is equivalent to 4 dollars.

Find the total cost by multiplying this by 20:

20(4)

= 80

So, the largest price to print 20 copies is $80

A 5 ounce bottle of juice cost $1.35 and an 8 ounce bottle of juice cost $2.16 a what is the unit cost per ounce of juice and b what is the better buy

Answers

Answers:

First bottle's unit cost = 27 cents per oz

Second bottle's unit cost = 27 cents per oz

Both have the same unit cost.

----------------------------------------

Work Shown:

unit cost = price/(number of ounces)

1st bottle unit cost = (1.35)/(5) = 0.27 dollars per oz = 27 cents per oz

2nd bottle unit cost = (2.16)/(8) = 0.27 dollars per oz = 27 cents per oz

Both lead to the same unit cost. Therefore, you can pick either option and it doesn't matter.

3. What is the length of a rectangle with a width of 1.2 m and an area of 2.4 m2 m ?​

Answers

Step-by-step explanation:

area=length×width

2.4=x×1.2

1.2x=2.4

x=2.4÷1.2

x=2

therefore width = 2cm

The length of the rectangle is 2 meters.

We have,

Width of rectangle= 1.2m

Area of rectangle = 2.4 m²

To find the length of a rectangle when given its width and area, you can use the formula:

Length = Area / Width

So, the length rectangle

Length = 2.4 m² / 1.2 m

Length = 2 meters

Therefore, the length of the rectangle is 2 meters.

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give ABCD is a trapizod , Ab = 13, CD= 14, BC = 15, and AD = 20 what is the area

Answers

Step-by-step explanation:

A=140sq. units

Step-by-step explanation:

ABCD

A=13

B=15

C=14

D=20

C=14×14

=196sqr.units

A rational expression is​ _______ for those values of the​ variable(s) that make the denominator zero.

Answers

9514 1404 393

Answer:

  undefined

Step-by-step explanation:

A rational expression is undefined when its denominator is zero.

A zookeeper published the following stem-and-leaf plot showing the number of lizards at each major zoo in the country:

0
1
2
3
4
5
6


0
6
8
8
8
0
2
6
6
7
8
1
2
6
6



















00
10
20
30
40
50
60




















0
0
0
0
1
0
0


6
2
2


8
6
6


8
6
6


8
7
0


0
8


0


Key:
2



0
=
20
2∣0=202, vertical bar, 0, equals, 20 lizards
How many zoos have more than 26 lizards

Answers

do you have a picture or something ? this isn’t helping me.

Write 36 as a product of its prime factors.Write the factors in order,from smallest to largest.

Pls Help me!!!!

Answers

Answer:

2×2×3×3

Step-by-step explanation:

Answer:

2×2×3×3

Step-by-step explanation:

36=3×12

12=3×4

4=2×2

=3×3×2×2

Hope this helps! <3

Given the parent graph h(x) = x, what happens when it is changed to h(x + 9)?

Answers

Answer:

If the parent graph is h(x) = x, then h(x+9) would actually be shifting the graph 9 units to the LEFT.

Let me know if this helps!

Can someone please help me solve the equation?

Answers

Answer:

(0,0) is the x and y intercept of the function

Step-by-step explanation:

The parabola touches the x and y axis at 0

The x intercept is (0,0) and the y intercept is (0,0)

Answer:

(0, 0) is the x and y intercepts

Step-by-step explanation:

intercepts are where the curve of the equation contacts an axis

The equation is y = x²

Determine the remaining sides and angles of the triangle ABC.
c=6 mi, B = 38.71°, C = 32.51°
Find the measure of angle A.
A=°
(Type an integer or a decimal.)
Find the length of side a.
а:
mi
(Round to the nearest mile as needed.)
Find the length of side b.
b=mi
(Round to the nearest mile as needed.)

Answers

9514 1404 393

Answer:

  A = 108.78°

  a = 11 mi

  b = 7 mi

Step-by-step explanation:

The sum of angles in a triangle is 180°, so the third angle is ...

  A = 180° -38.71° -32.51°

  A = 108.78°

__

The remaining sides can be found from the law of sines.

  a/sin(A) = c/sin(C)

  a = sin(A)·c/sin(C) ≈ 0.946762 × 11.163896

  a ≈ 11 mi

  b = sin(B)·11.163896 ≈ 0.625379 × 11.163896

  b ≈ 7 mi

Translate and solve: five less than z is 4

Answers

z -5 =4

neutralize the left -5 by adding 5 on both sides

z -5 (+5) = 4 (+5)

z = 9

A cash register contains $10 bills and $50 bills with a total value of $1080.If there are 28 bills total, then how many of each does the register contain?

Answers

Answer:

8 ten dollar bills

20 fifty dollar bills

Step-by-step explanation:

x = number of 10 dollar bills

y = number of 50 dollar bills

x+y = 28

10x+50y = 1080

Multiply the first equation by -10

-10x -10y = -280

Add this to the second equation

-10x -10y = -280

10x+50y = 1080

-----------------------

 40y = 800

Divide by 40

40y/40 = 800/40

y = 20

Now find x

x+y =28

x+20 = 28

x = 28-20

x= 8

Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem. (Enter your answers as a comma-separated list.) F(x) = sin(x/2) , [π/2,3π/2]

Answers

Answer:

The numbers 3(pi)/2, 5(pi)/2 satisfy the conclusion of Rolle's Theorem

Step-by-step explanation:

1. The function must be continuous.  

Trigonometric functions are continuous.  

2.  It must be true that f(a) = f(b) = 0

For this case sin(pi) = sin(3pi) = 0

3. Therefore by Rolle's Theorem, there exist a point, x, such that f(x) = 0

For this case f(x) = cos(x)

And cos(x) = 0 at x = 3(pi)/2,5(pi)/2

fernando charges a flat fee of 4.50 plus 2.00 per mile for his taxi service, when he got to the airport the cab fare was 12.50 how many miles was the trip to the airport

Answers

the trip to the airport was 6.25 miles.

The trip was 6.25miles long

If we add one unit to the length (l) of a rectangle that has width (w), what is its new area (NA) in terms of its old area (A)?
NA = A x w
NA = A + w
NA = A + l
NA = A

Answers

NA = A + W

By adding one unit to length, we increase the overall area by the width of the rectangle. This is because the formula for the area of a rectangle is A = l x w. So, NA = (l + 1) x w = (l x w) + w = A + w.

URGENT! 15 PNTS
Points T, R, and P, define _____

A. plane B
B. line e
C. line segment PR⎯⎯⎯⎯⎯⎯⎯
D. plane M

Answers

Answer:

Since points T, R, and P are all present on plane B, the answer is A.

Points T, R, and P define plane B

We have given that,

A. plane B

B. line e

C. line segment PR⎯⎯⎯⎯⎯⎯⎯

D. plane M

We have to determine the Points T, R, and P, define

What is the plane?

A plane is a two-dimensional doubly ruled surface spanned by two linearly independent vectors. The generalization of the plane to higher dimensions is called a hyperplane. The angle between two intersecting planes is known as the dihedral angle.

Since points T, R, and P are all present on plane B, the answer is A

Points T, R, and P define plane B.

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A company pays a bonus to four employees A, B, C, and D. A gets four times as much as B. B gets 50% of the amount paid to C. C and D get the same amount. If the total bonus is ¢1,800.00, set all necessary equations to ascertain the share of each employees.

Answers

Answer:

A = 800, B = 200, C = 400 Andy D = 400

Step-by-step explanation:

The surface area of a cylinder?

Answers

Answer:

18. 84 ft² or 18.85 ft² when rounded to the nearest tenth

Step-by-step explanation:

2πrh+2πr²

2× 3.14 × 1 × 2= 12.56

2 × 3.14 × 1² = 6.28

12.56 + 6.28 = 18.84

Have a great day :)

Answer:

18.85 [tex]ft^2\\[/tex]

*You should run the numbers yourself as well. Sometimes different calculators will get marginally different numbers or use a different rounding for [tex]\pi[/tex] that gives a slightly different answer*

Step-by-step explanation:

Surface area of a cylinder: [tex]2\pi rh+2\pi r^2[/tex]

Where h is the height and r is the radius. Remember that the radius is half the diameter, and the diameter is a straight line that passes through a circle.

I could be wrong, but I think you had the correct equation but used the diameter in stead of the radius to get 50.36.

Radius: 1   Height: 2

Plug numbers into equation:

[tex]A=2\pi (1)(2)+2\pi (1)^2= 18.8495. . .[/tex]

I hope that helps!

Please Help me! I will mark brainliest for correct answer!!!

Answers

Answer:

y=2/3x+1

Step-by-step explanation:

The life of light bulbs is distributed normally. The standard deviation of the lifetime is 2525 hours and the mean lifetime of a bulb is 590590 hours. Find the probability of a bulb lasting for at most 622622 hours. Round your answer to four decimal places.

Answers

Answer:

0.8997 = 89.97% probability of a bulb lasting for at most 622 hours.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 590 hours, standard deviation of 25 hours.

This means that [tex]\mu = 590, \sigma = 25[/tex]

Find the probability of a bulb lasting for at most 622 hours.

This is the p-value of Z when X = 622.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{622 - 590}{25}[/tex]

[tex]Z = 1.28[/tex]

[tex]Z = 1.28[/tex] has a p-value of 0.8997.

0.8997 = 89.97% probability of a bulb lasting for at most 622 hours.

i would like some help please i am stuck ​

Answers

Answer: -2(d) is the answer.

Step-by-step explanation:

x1 = 3

y1 = -5

x2 = -2

y2 = 5

slope (m) = rise/run = (y2 - y1)/(x2-x1)

                                =(5-(-5))/(-2-3)

                                 =   10/-5

                                 = -2

8
6
4
2
6
8
-8 -6 -4 -2 0-3
21
.
-6
-8
O A. y -[x]-2
OB. y -[x]+3
O C. y = (x) - 3
O D. y = [x]+2

Answers

The required equation of the line is y = [x]+2

From the graph shown, we can see that the line dotted points forms a straight line. We are to find the required equation of the line formed.

The formula for calculating the equation of a straight line is expressed as

y = mx+b where

m is the slope b is the y-intercept

Get the slope 'm'

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Using the coordinate points (2, 0) and (4, 2)

[tex]m=\frac{2-0}{4-2}\\m=\frac{2}{2}\\m=1[/tex]

Get the y-intercept 'b'

Substitute m = 1 and (2, 0) into y = mx+b as shown;

[tex]2=1(0)+b\\2=0+b\\b=2[/tex]

Get the required equation. Recall that y = mx+b, hence;

[tex]y = 1x + 2\\y=x+2[/tex]

Hence the required equation of the line is y = [x]+2

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Assume that x and y are both differentiable functions of t. Find dx/dt when x=11 and dy/dt=-4 for the equation xy=99 .

Answers

Differentiating both sides of

xy = 99

with respect to t yields

x dy/dt + y dx/dt = 0

When x = 11, we have

11y = 99   ==>   y = 9

and we're given that dy/dt = -4 at this point, which means

11 (-4) + 9 dx/dt = 0   ==>   dx/dt = 44/9

PLEASE HELP NOW

Solve the equation for y. Identify the slope and y-intercept then graph the equation.

2y-3x=10

Y=
M=
B=

Please Include a picture of the graph and show your work if you can

Answers

Answer:

Step-by-step explanation:

Solve for y:

[tex]2y-3x=10\\2y=3x+10\\y=\frac{3}{2} x+5[/tex]

Therefore:

y = 3/2x + 5

m = 3/2

b = 5

Graph below courtesy of Desmos.

Ilang litro ng tubig ang kailangang isalin sa timba na naglalaman ng 10 000 mililitro

Answers

Answer

nghiệmTrảingu       từng bước:

A movie theater has a seating capacity of 187. The theater charges $5.00 for children, $7.00 for students, and $12.00 of adults. There are half as many adults as there are children. If the total ticket sales was $ 1338, How many children, students, and adults attended?
___ children attended.
___ students attended.
___ adults attended.

Answers

Answer:

A) children attended=98 b) students attended=60 c)adults attended=49

Step-by-step explanation:

system%28a%2Bc%2Bx=207%2Cc%2Fa=2%2C5c%2B7x%2B12a=1498%29

Simplify and solve the system.

-

a%2B2a%2Bx=207

3a%2Bx=207

x=207-3aandc=2a

-

The revenue equation can be written in terms of just one variable, a.

10a%2B7%28207-3a%29%2B12a=1498

Solve for a;

use it to find x and c.

FURTHER STEPS

-

10a%2B1449-21a%2B12a=1498

a%2B1449=1498

a=98-49

highlight%28a=49 -------adults

-

c=2a

c=2%2A49

highlight%28c=98 -------children

-

x=207-a-c

x=207-49-98

highlight%28x=60 ---------students

prove that Sin^6 ϴ-cos^6ϴ=(2Sin^2ϴ-1)(cos^2ϴ+sin^4ϴ) please sove step by step with language it is opt maths question please sove i will mark you the best ​

Answers

Answer:

hshdkKnfbsjfjznd jzkz e zkkfkd

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Dale Rolfe, a supporter of ethical voluntourism, explains the shocking reality that "Animal sanctuaries and orphanages are often manufactured for the voluntourist...encouraging a cycle of exploiting the very animals and children the volunteers are trying to help."[3] Proponents of the "volunteer plus travel" experience also argue that traveling to new places builds character and is a valuable way to learn about different cultures. With voluntourism, however, participants often pursue experiences that are all about them. For example, they sign up to build a school for a gold star on their resume, but they have no real building skills and take jobs away from local construction workers (Schulten). Or, they arrive to teach English but instead take selfies with the locals. 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